Calculator Input
Example Data Table
This built-in example uses a temperature of 5800 K and wavelength values in micrometers.
| Temperature (K) | Wavelength (µm) | Spectral Radiance Bλ (W·sr⁻¹·m⁻³) |
|---|---|---|
| 5,800.00 | 0.25 | 5.982995e+12 |
| 5,800.00 | 0.50 | 2.688220e+13 |
| 5,800.00 | 0.75 | 1.907102e+13 |
| 5,800.00 | 1.00 | 1.087807e+13 |
| 5,800.00 | 2.00 | 1.515022e+12 |
| 5,800.00 | 5.00 | 5.933401e+10 |
Formula Used
Planck law in wavelength form:
Bλ(λ,T) = (2hc² / λ⁵) / (exp(hc / (λkT)) - 1)
Planck law in frequency form:
Bν(ν,T) = (2hν³ / c²) / (exp(hν / (kT)) - 1)
Wien displacement relation:
λmax = b / T
Stefan-Boltzmann relation:
M = σT⁴
Band radiant exitance for the chosen range:
Mband ≈ π ∫ B dλ or Mband ≈ π ∫ B dν
This calculator numerically evaluates the selected spectrum using the trapezoidal rule over the generated sample points.
How to Use This Calculator
1. Enter the blackbody temperature in kelvin.
2. Choose wavelength mode or frequency mode.
3. Select the matching unit and set the start, end, and target value.
4. Choose how many samples should be generated for the spectrum curve.
5. Submit the form to see the result cards, graph, data table, and export buttons.
6. Use the CSV or PDF buttons to save the computed spectrum and summary values.
FAQs
1. What is blackbody radiance?
Blackbody radiance is the ideal spectral intensity emitted by a perfect absorber and emitter at thermal equilibrium. It depends only on temperature and the chosen spectral variable.
2. Why can I calculate by wavelength or frequency?
Planck’s law can be written in either domain. Both describe the same physical source, but their curves and peak locations differ because the variables scale differently.
3. What does the target value represent?
The target value is the specific wavelength or frequency where the calculator reports a single-point spectral radiance result, in addition to the full generated spectrum.
4. Why does the peak move when temperature increases?
As temperature rises, the spectrum shifts toward shorter wavelengths and higher frequencies. This behavior follows Wien’s displacement law and reflects hotter bodies radiating more intensely.
5. What is band radiant exitance?
Band radiant exitance is the emitted power per unit area across your selected spectral range. This calculator estimates it by integrating radiance and multiplying by π.
6. Is band exitance the same as total emitted power?
No. Band exitance covers only the chosen interval. Total exitance comes from the Stefan-Boltzmann law and includes all wavelengths or all frequencies.
7. Why are the outputs shown in scientific notation?
Radiance values can be extremely large or extremely small. Scientific notation keeps the results readable and helps compare data across wide thermal ranges.
8. Can I use this for real materials?
This page models an ideal blackbody. Real surfaces usually emit less, so practical material estimates often need emissivity corrections applied outside this idealized calculation.